If you want something simple that does a little more than just validates format, but doesn't go as far as validating how many days is in the month that is entered, or leap years, you can use this:
^(19|20)[0-9]{2}-(0[1-9]|1[0-2])-(0[1-9]|[12][0-9]|3[01])$
This example allows years 19xx and 20xx